{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UY2SI4BJIYDTNC5CKDXCYBV3DR","short_pith_number":"pith:UY2SI4BJ","canonical_record":{"source":{"id":"1209.3180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-14T13:22:53Z","cross_cats_sorted":[],"title_canon_sha256":"9226f4eb339f1062fe4241f64eba5e6be0c170cb3d6d85e2e9095bb06a58757b","abstract_canon_sha256":"fdeaa3cb211c19c286634a5e09d251ad865e17dcf502b255479dd8f3c0bbc71e"},"schema_version":"1.0"},"canonical_sha256":"a6352470294607368ba250ee2c06bb1c6b3a2cf39b7f8b8d2a913314c89d4aa7","source":{"kind":"arxiv","id":"1209.3180","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3180","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3180v1","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3180","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"pith_short_12","alias_value":"UY2SI4BJIYDT","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UY2SI4BJIYDTNC5C","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UY2SI4BJ","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UY2SI4BJIYDTNC5CKDXCYBV3DR","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-14T13:22:53Z","cross_cats_sorted":[],"title_canon_sha256":"9226f4eb339f1062fe4241f64eba5e6be0c170cb3d6d85e2e9095bb06a58757b","abstract_canon_sha256":"fdeaa3cb211c19c286634a5e09d251ad865e17dcf502b255479dd8f3c0bbc71e"},"schema_version":"1.0"},"canonical_sha256":"a6352470294607368ba250ee2c06bb1c6b3a2cf39b7f8b8d2a913314c89d4aa7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:32.609784Z","signature_b64":"GAgnOWuDbQJ9vftMKJqCldWyysLVl2gsQEdsZR+CwRjFWsnIBsN5mX3WkFSlw9XnJxjA28cHMRRK7fkTcnfSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6352470294607368ba250ee2c06bb1c6b3a2cf39b7f8b8d2a913314c89d4aa7","last_reissued_at":"2026-05-18T03:45:32.609013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:32.609013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3180","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Un+SjqbPqglUccpjOpjT7z/O/lRW3McncxGLGgz1eV/ckXvF+AGwnoRfz7Aqky8tJ9tePcVMg4GvGeFxLi+UCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:13:55.811756Z"},"content_sha256":"56cae5bbbc8bdc4054bbee140e23ed1b8ea1bb5242a333fd1e5b1de8f3c8f51b","schema_version":"1.0","event_id":"sha256:56cae5bbbc8bdc4054bbee140e23ed1b8ea1bb5242a333fd1e5b1de8f3c8f51b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UY2SI4BJIYDTNC5CKDXCYBV3DR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Filtered Az\\'ema martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Umut \\c{C}etin","submitted_at":"2012-09-14T13:22:53Z","abstract_excerpt":"We study the optional projection of a standard Brownian motion on the natural filtration of certain kinds of observation processes. The observation process, $Y$, is defined as a solution of a stochastic differential equation such that it reveals some (possibly noisy) information about the signs of the Brownian motion when $Y$ hits 0. As such, the associated optional projections are related to Az\\'ema's martingales which are obtained by projecting the Brownian motion onto the filtration generated by observing its signs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3180","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YKsPOdoRpH3SPmGyHvQPleFcwokKludNO7mbtfuK+O7pBhYkXV5I+0hrAC47NqGFeGFy1yWAdhRwnBI6mlAzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:13:55.812112Z"},"content_sha256":"fbfca64baeea3518910d0d92f866a64aa5e3a7e7199dceb83d30703cad364a9b","schema_version":"1.0","event_id":"sha256:fbfca64baeea3518910d0d92f866a64aa5e3a7e7199dceb83d30703cad364a9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UY2SI4BJIYDTNC5CKDXCYBV3DR/bundle.json","state_url":"https://pith.science/pith/UY2SI4BJIYDTNC5CKDXCYBV3DR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UY2SI4BJIYDTNC5CKDXCYBV3DR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T02:13:55Z","links":{"resolver":"https://pith.science/pith/UY2SI4BJIYDTNC5CKDXCYBV3DR","bundle":"https://pith.science/pith/UY2SI4BJIYDTNC5CKDXCYBV3DR/bundle.json","state":"https://pith.science/pith/UY2SI4BJIYDTNC5CKDXCYBV3DR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UY2SI4BJIYDTNC5CKDXCYBV3DR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UY2SI4BJIYDTNC5CKDXCYBV3DR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fdeaa3cb211c19c286634a5e09d251ad865e17dcf502b255479dd8f3c0bbc71e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-14T13:22:53Z","title_canon_sha256":"9226f4eb339f1062fe4241f64eba5e6be0c170cb3d6d85e2e9095bb06a58757b"},"schema_version":"1.0","source":{"id":"1209.3180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3180","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3180v1","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3180","created_at":"2026-05-18T03:45:32Z"},{"alias_kind":"pith_short_12","alias_value":"UY2SI4BJIYDT","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UY2SI4BJIYDTNC5C","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UY2SI4BJ","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:fbfca64baeea3518910d0d92f866a64aa5e3a7e7199dceb83d30703cad364a9b","target":"graph","created_at":"2026-05-18T03:45:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the optional projection of a standard Brownian motion on the natural filtration of certain kinds of observation processes. The observation process, $Y$, is defined as a solution of a stochastic differential equation such that it reveals some (possibly noisy) information about the signs of the Brownian motion when $Y$ hits 0. As such, the associated optional projections are related to Az\\'ema's martingales which are obtained by projecting the Brownian motion onto the filtration generated by observing its signs.","authors_text":"Umut \\c{C}etin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-14T13:22:53Z","title":"Filtered Az\\'ema martingales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3180","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:56cae5bbbc8bdc4054bbee140e23ed1b8ea1bb5242a333fd1e5b1de8f3c8f51b","target":"record","created_at":"2026-05-18T03:45:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fdeaa3cb211c19c286634a5e09d251ad865e17dcf502b255479dd8f3c0bbc71e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-09-14T13:22:53Z","title_canon_sha256":"9226f4eb339f1062fe4241f64eba5e6be0c170cb3d6d85e2e9095bb06a58757b"},"schema_version":"1.0","source":{"id":"1209.3180","kind":"arxiv","version":1}},"canonical_sha256":"a6352470294607368ba250ee2c06bb1c6b3a2cf39b7f8b8d2a913314c89d4aa7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6352470294607368ba250ee2c06bb1c6b3a2cf39b7f8b8d2a913314c89d4aa7","first_computed_at":"2026-05-18T03:45:32.609013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:32.609013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GAgnOWuDbQJ9vftMKJqCldWyysLVl2gsQEdsZR+CwRjFWsnIBsN5mX3WkFSlw9XnJxjA28cHMRRK7fkTcnfSCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:32.609784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56cae5bbbc8bdc4054bbee140e23ed1b8ea1bb5242a333fd1e5b1de8f3c8f51b","sha256:fbfca64baeea3518910d0d92f866a64aa5e3a7e7199dceb83d30703cad364a9b"],"state_sha256":"7fa0a2b2f843488ad28c4db052714ebf221955b3f06c75907fb1888d2fa79fb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Cuw20HFAM1tOEorVpHoWMwHUwsLnyohG5wHMB6jlW6W5uqGcBjwTVuRuq+ZP4MbUDLj5MR+DwPSl9OEOjZVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T02:13:55.814100Z","bundle_sha256":"c25313488aff3dae0cff4c681969496e82d2c03129446653199f8ea8e3d2a8eb"}}